The present invention relates in general to web forming processes and, more particularly, to improved two-dimensional web property variation by means of modeling web property variations using functional transformation and controlling web property variations with two-dimensional optimal predictive controllers. "Dimensional" as used herein refers to the number of independent variables such that if a dependent variable y is plotted versus an independent variable x, the plot will be referred to as one-dimensional; if a dependent variable z is plotted versus two independent variables x and y, the plot will be referred to as two-dimensional; and so forth.
Machines and processes which produce webs of sheet material, such as paper, plastic and aluminum, encounter common control problems in producing webs which satisfy required specifications for characteristics for a given product. Specifications commonly include required ranges for thickness, moisture content, weight per unit area, smoothness and the like. Quality control is complicated by the fact that characteristics vary in both the machine direction (MD) or direction of movement of the web through a machine as it is being produced and in the machine cross direction (CD) or lateral direction across the machine or web.
The MD variations in the web are affected by factors which impact the entire width of the web including, for example, the source of materials being used to form the web, other common supplies used to produce the web such as steam, the speed of the machine producing the web, and other similar factors. On the other hand, CD variations are controlled by arrays of actuator devices which are distributed across the width of the machine producing the web. On paper making machines, for which the present invention is particularly applicable and initially being applied, the CD actuator devices include slice lip actuators which are adjusted to control the slice of a headbox, dilution valves, steam showers, heaters, calenders, and other known devices.
Cross-direction (CD) profile control has been used to improve CD uniformity in many web forming processes including paper making machines, as well as plastic film extruders, sheet calenders, coaters and similar machines. Due to the speed and resolution limits of web scanning measurements, CD control actions are usually applied infrequently. Thus, long term or steady-state CD profile uniformity has been generally satisfactory in existing CD control arrangements.
However, there is a growing demand for better short-term profile uniformity in many sheet-making processes. One example of this demand in the paper making industry is the desire to produce uniform and sellable paper almost immediately after any process transition such as machine start-up, product grade change, sheet break recovery, and the like. The demand for more responsive web uniformity has also intensified due to the arrival of new stationary full-width sheet property measurement, see U.S. Pat. No. 5,563,809 which is incorporated herein by reference. Unfortunately, existing CD profile control arrangements can not satisfy this demand due to the massive amounts of memory and real-time processing required.
A new control technique is thus needed to satisfy these demands and to make sheet-forming processes achieve true two-dimensional uniformity responsively. Preferably, the new control technique would correct conventional CD variations and also some residual variations which previously have gone uncorrected.